# What is a ring current transformer

## Power converter

A Power converter is a transformer which is used for the galvanically isolated measurement of currents.

### Passive current transformer 

A passive current transformer consists of a toroidal core. The cable of the current to be measured is led through the hole in the toroidal core and forms the primary winding with one turn. The secondary winding with approx. 100-1000 turns is located on the toroidal core. The secondary winding is always equipped with a low-resistance measuring resistor (load resistance). shunt) completed; typical values ​​are between 10Ω and 200Ω.

In principle, this current transformer works like a normal transformer, but with somewhat exotic values, which sometimes makes it difficult to understand. On the one hand, the output voltage is quite small, typically 0.5V – 2V. On the other hand, the input current is quite high, from a few amps to the kiloampere range. The current is transformed down according to the known transformer formula in the ratio of the number of turns:

[math] \ displaystyle {I_A = \ frac {I_E} {N}} [/ math]
• [math] \ displaystyle {I_A} [/ math]: output current
• [math] \ displaystyle {I_E} [/ math]: input current
• [math] \ displaystyle {N} [/ math]: Number of turns of the secondary winding

However, this only applies if the shunt is not too high-resistance and the converter does not saturate due to an input current that is too high. Since it is a normal transformer, it can only transform alternating currents. The lower and upper limit frequency depends on the core material and the structure. Typically there are current transformers for network applications with 50/60 Hz as well as for switching power supplies in the range 20kHz – 500kHz.

A current transformer almost always acts like a constant current source, at least as long as it does not go into saturation. That means, for example, you can connect a bridge rectifier directly and a DC meter behind it. The voltage drop of the diodes does not matter, a precision rectifier with operational amplifiers is not necessary. However, it must not cause the output voltage to rise too much, because then saturation threatens again.

If you want to increase the sensitivity of a current transformer, you can run the line on the primary side several times through the ring core, as far as this is mechanically possible. This multiplies the sensitivity by the factor M., the number of primary turns. The price for this is that the measuring range can also be increased by a factor of 1 /M. gets smaller.

### Active current transformer 

An active current transformer is also based on a toroidal core. However, it does not measure the cable's magnetic field with a secondary coil, but with a Hall sensor that is inserted into a slot in the toroidal core. This can also be used to measure direct current. The disadvantage is the higher effort and thus the price as well as the need for a power supply.

### Current clamp 

A current clamp is constructed similarly to an active current transformer, except that the toroidal core can be opened to allow a cable to be passed through. Depending on the type, current clamps can only measure alternating current or also direct current.

### Calculation of the parameters 

In principle, a current transformer is calculated like a normal transformer. In principle, the calculation can be made from the primary as well as the secondary side. In practice, the secondary side is advantageous because almost all important parameters can be specified and calculated directly here.

### Number of turns 

First you have to determine how large the number of turns N should be, because it defines the transmission ratio. If you want to measure large currents, you usually need many turns, because you want the smallest possible, manageable currents on the secondary side.

### Output voltage 

The shunt determines how much output voltage is directly available. On the one hand, a high output voltage is desirable in order to be able to feed an evaluation circuit such as a rectifier or AD converter, if possible without amplification. On the other hand, a relatively large core with a large cross section is required for high output voltages. The relationship between input current, output voltage and shunt is very simple.

[math] \ displaystyle {U_A = \ frac {I_E} {N} \ cdot R_S} [/ math]
• [math] \ displaystyle {R_S} [/ math]: measuring resistor
• [math] \ displaystyle {U_A} [/ math]: output voltage, rms value
• [math] \ displaystyle {I_E} [/ math]: input current, rms value

### Core size 

The core must have a sufficient cross-section so that it does not go into saturation with the selected number of turns and output voltage. The basic transformer formula gives an answer here quickly and easily. To do this, however, you have to know how much flux density the respective material can withstand. This value can be found in the data sheet. If this is not available, standard values ​​can be assumed (ferrite approx. 0.3T, iron powder approx. 0.5T, transformer iron approx. 1.5T)

[math] \ displaystyle {N = \ frac {U_A} {4.44 \ times f \ times A \ times B}} [/ math]
• f: frequency (formula applies to sinusoidal signals)
• [math] \ displaystyle {A} [/ math]: Magnetic cross section of the core
• [math] \ displaystyle {B} [/ math]: Magnetic flux density

This is the minimum number of turns that the core with this cross-section needs. More does not hurt, with less the core goes into saturation at full modulation. If you still want to use a small core, you have to reduce the output voltage, i.e. choose a smaller shunt. If you want to use a very small shunt, it usually makes sense to use a transimpedance amplifier. This has an input resistance of practically zero ohms. However, one must not forget the ohmic resistance of the secondary winding, this can be several dozen ohms, especially in the case of small current transformers with a large number of turns. This then acts as a limit for lowering the shunt resistance.

### Core material

The core material determines the inductance of our transformer. Here, too, it applies that a very high inductance is necessary for low frequencies in order to keep the magnetizing current small. Because this flows in addition to the measurement current and falsifies the measurement result. The inductance can easily be calculated.

[math] \ displaystyle {L = A_L \ cdot N ^ 2} [/ math]

The [math] \ displaystyle {A_L} [/ math] value is given in the data sheet of the toroidal core, when recycling toroidal cores you have to measure it, see article Coil. With the help of the inductance it is just as easy to calculate the reactance at the working frequency and the reactive current (magnetizing current) via the output voltage.

[math] \ displaystyle {X_L = 2 \ cdot \ pi \ cdot f \ cdot L} [/ math]
[math] \ displaystyle {I_M = \ frac {U_A} {X_L}} [/ math]

It must be noted that the measuring current and magnetizing current are phase shifted by 90 degrees, i.e. they must be added geometrically (complex numbers, vector diagram). That means, however, that even a magnetizing current of 10% only has an effect of approx. 5% total error.

[math] \ displaystyle {F_M = (\ frac {\ sqrt {I_M ^ 2 + I_A ^ 2}} {I_A} -1) \ cdot 100 \%} [/ math]
• [math] \ displaystyle {F_M} [/ math]: measurement error

At higher frequencies in the kHz range, lower permeabilities will be used, which also has a positive effect on reducing the leakage inductance and thus increases the upper limit frequency at the expense of the lower limit frequency.

### Example 

Let us assume that we want to develop a current transformer for 50 Hz mains current ourselves. The nominal current should be 16A, which is the maximum value that can be taken from a normal socket. We want to get 2V as output voltage, both values ​​are effective values. We want to use the type TN20 / 10 / 7-3E25 from Ferroxcube as a usable toroidal core, it has an inner diameter of 9mm and a cross-section of 33.6mm2 and a [math] \ displaystyle {A_L} [/ math] value of 5340 nH / N². It's a ferrite core.

The minimum number of turns is calculated from.

[math] \ displaystyle {\ begin {align} N & = \ frac {U} {4.44 \ times f \ times A \ times B} \ & = \ frac {2 \ text {V}} {4, 44 \ times 50 \ times 33.6 \ times 10 ^ {- 6} \ text {m} ^ 2 \ times 0.3 \ text {T}} = 893 \ end {align}} [/ math]

So we decide on 1000 turns, which simplifies the calculation. This results in our shunt resistance too

[math] \ displaystyle {\ begin {align} R_S & = \ frac {U_A \ cdot N} {I_E} \ & = \ frac {2 \ text {V} \ cdot 1000} {16 \ text {A}} = 125 \ Omega \ end {align}} [/ math]

We choose the standard value 120Ω.

Finally, we check the error caused by the reactive current.

[math] \ displaystyle {\ begin {align} L & = A_L \ cdot N ^ 2 \ & = 5340 \ frac {nH} {N ^ 2} \ cdot 1000 ^ 2 = 5,34H \ end {align}} [/ math]

5.3 are H. very much.

[math] \ displaystyle {\ begin {align} X_L & = 2 \ cdot \ pi \ cdot f \ cdot L \ & = 2 \ cdot \ pi \ cdot 50 \ text {Hz} \ cdot 5.34 \ text { H} = 1677 \ Omega \ end {align}} [/ math]
[math] \ displaystyle {\ begin {align} I_M & = \ frac {U_A} {X_L} \ & = \ frac {2 \ text {V}} {1677 \ Omega} = 1,2 \ text {mA} \ end {align}} [/ math]
[math] \ displaystyle {\ begin {align} F_M & = \ Bigl (\ frac {\ sqrt {I_M ^ 2 + I_A ^ 2}} {I_A} -1 \ Bigr) \ cdot 100% \ & = \ Bigl (\ frac {\ sqrt {1,2 \ text {mA} ^ 2 + 16 \ text {mA} ^ 2}} {16 \ text {mA}} - 1 \ Bigr) \ cdot 100% = 2.8% \ end {align}} [/ math]

The transformed nominal current is 16mA, the magnetizing current 1.2mA or 7.5%, which results in a total error of 2.8%.

### Applications 

• Residual current switch (FI switch)
• Instrument transformers for high to very high currents (welding machines, chargers)
• Instrument transformers for high voltage isolation (high voltage networks)
• Instrument transformers in switching power supplies
• Clamp meter